How do you solve the following exponential equation by expressing each power of the same base and then equating the exponents?6^x-3/4= square rot of 6

Answers

Answer 1

Answer: Start by switching everything into exponent form: 6^(x-3/4)=6^(1/2). In this equation, we're trying to find the value of x that will make each side equal. Because the base (6) is the same on either side of the equal sign, all we need to worry about is the exponents, because this equation can only be true if the exponents are the same (i.e. 6^(1/2)=6^(1/2)). Thus, you can actually ignore the 6's entirely and only focus on the exponents: x-3/4=1/2. Then, this has just become a simple algebraic expression. x-3/4+3/4=1/2+3/4. x=1/2(2/2)+3/4. x=2/4+3/4. x=5/4

Answer 2

Answer: $6^{x-\tfrac{3}{4}}=√(6)\n6^{x-\tfrac{3}{4}}=6^{\tfrac{1}{2}}\nx-(3)/(4)=(1)/(2)\nx=(1)/(2)+(3)/(4)\nx=(2)/(4)+(3)/(4)\nx=(5)/(4)$

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Answers

Answer:

$x=7.4$ m and $x=11.2$ m

Step-by-step explanation:

To do these problems, we will need to use the Pythagorean Theorem.

Recall that it states $a^2+b^2=c^2$ , where c is the longest side, the hypotenuse, of the triangle.

a) We have a triangle with side lengths 4.2 m and 6.1 m. These two sides correspond to a and b in this equation.

Now, we can plug these values into the equation and solve for c, which is x.

$(4.2)^2+(6.1)^2=x^2\n\n17.64+37.21=x^2\n\nx=√(54.85)\n\nx=7.406\n\nx=7.4$

b) We have a triangle with side lengths 5.1 m and 12.3 m. These sides correspond to a and c, so b will be x.

Now, we can plug these values into the equation and solve for x.

$(5.1)^2+x^2=(12.3)^2\n\n26.01+x^2=151.29\n\nx=√(151.29-26.01)\n\nx=√(125.28)\n\nx=11.193\n\nx=11.2$

Answer:

Step-by-step explanation:

Formula: A squared + B squared = C squared

For the first question:

4.2 squared = 17.64

6.1 squared = 37.21

17.64+37.21 = 54.85

C squared = 54.85

The square root of 54.85 = 7.4

So, x = 7.4 m

For the second question:

5.1 squared = 26.01

12.3 squared = 151.29

26.01 + 151.29 = 177.3

C squared = 177.3

The square root of 177.3 = 13.3

So, x = 13.3 m

Hope this helps!

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Answers

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Answers

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